Bernstein多项式及其幻曲面

Bernstein Polynomial and Magic Surfaces

文中研究的幻曲面是指以任何数字幻方 (矩阵 )为型值的Bernstain B啨ｚｉｅｒ曲面 这类曲面所特有的积分不变量反映了这类曲面的某种“能量守恒性” ,针对它潜在的应用价值进行了进一步的理论探讨 证明了二次幻曲面是一个高斯曲率非正的曲面 ,且仅有一点高斯曲率为 0

The so called magic surfaces are some Bernstein Bezier surfaces with certain magic square as their control matrixes This kind of surfaces presents some intrinsic invariant of energe conservation of surface, and their potential applications are explored Some geometrical properties of magic surfaces are illustrated It is proved that any magic surface of second degree has non positive Gaussian curvature Approach to smooth connection of magic surfaces is discussed